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It is a famous result of Lovasz and Yemini (1982) that 6-connected graphs arerigid in the plane. This was recently improved by Jackson and Jordan (2009) whoshowed that 6-mixed connectivity is also sufficient for rigidity. Here we givesufficient graph connectivity conditions for both `forced symmetric' and`incidentally symmetric' infinitesimal rigidity in the plane.

Sufficient connectivity conditions for rigidity of symmetric frameworks